Prank...Plank, plonk, plink
[Header Image Credit] Ishango Bone by African Odyssey via Pinterest.
It is 1st April 2025 today.
Presented in YYYYMMDD format, it is 20250401, which happens to be a prime. 401 is also a prime. To add a little, 2025 = 45² and 401 = 20² + 1.
Landau's fourth problem, which is open as of 31st March 2025, asked whether there are infinitely many primes which are of the form p = n²+1 for integer n (such as 101, 401, 1601, 8101,…).
The following is famous Borwein Integral. It is NOT a prank, but a very intriguing fact:
In the mathematical world, there are many hoaxes that use April Fool's Day as an excuse. Some of them have reached the state of the art. It occurred to me that someone might come up with a hoax by forging something similar to Borwein integral, by inserting a seemingly plausible but incorrect formula surreptitiously into a series of proven formulas by Srinivasa Ramanujan, or by inserting Apéry's constant in a transmogrified manner into an article on the Basel problem like inserting "not" into the historical record written in "The History of the Siege of Lisbon" by José Saramago, the recipient of the 1998 Nobel Prize in Literature.
Raimundo Silva, assigned to correct a book titled The History of Siege of Lisbon by his publishing house, decides to alter a crucial sentence by inserting the word "not" in the text, so that the book now claims that the Crusaders did not come to the aid of the Portuguese king in taking Lisbon from the Moors. This has repercussions, both for himself and for the historical profession. The plot also includes the love story between Raimundo Silva and his editorial supervisor Maria Sara.
However, such an effort would go down the path of nefarious attempts and eventually result in a forgery, conjuring up the Fraudulent Statistics Scandal 😱in 2018 by a ministry which is supposed to be healthy but filthy…
Let me share some healthy hoaxes:
① Martin Gardner on Ramanujan Integer (1975)
⬆️This is very famous, and has been cited in many places. It is not an elementary mathematics, as is explained (for example) in Joseph Silverman's "Advanced Topics in the Arithmetic of Elliptic Curves":
② Enrico Bombieri on Riemann Hypothesis (1997)
Date: Tue, 1 Apr 1997 12:35:12 -0500
Dear Doron,
There are fantastic developments to Alain Connes's lecture
at IAS last Wednesday. Connes gave an account of how to obtain
a trace formula involving zeroes of L-functions only on
the critical line, and the hope was that one could obtain also
Weil's explicit formula in the same context; this would solve
the Riemann hypothesis for all L-functions at one stroke. Thus there
cannot be even a single zeroe(1) off the critical line!
Well, a young physicist at the lecture saw in a flash that
one could set the whole thing in a combinatorial setting
using supersymmetric fermionic-bosonic systems (the physics
corresponds to a near absolute zero ensemble of a mixture
of anyons and morons with opposite spins) and, using the
C-based meta-language MISPAR, after six days of uninterrupted
work, computed the logdet of the resolvent Laplacian,
removed the infinities using renormalization, and, lo
and behold, he got the required positivity of Weil's explicit
formula! Wow!
Regards also from Paula Cohen.
Please give this the highest diffusion. Best,
Enrico
(1) This is the correct spelling, according to vicepresident Dan Quayle.
Enrico Bombieri, an Italian mathematician, was awarded the Fields Medal in 1974.
Alain Connes, a French mathematician, was awarded the Fields Medal in 1982, well-known for Noncommutative geometry (非可換幾何学).
③ Someone (widely believed to be Henri Darmon) on a counterexample to FLT (1994):
I wrote about Noam Elkies in the following article:
④ "The Mandelbrot Monk" article by Ray Girvan (1999)
This hoax reads
A retired Harvard university professor Bob Schipke was surprised by finding a picture of the Mandelbrot set in an illuminated manuscript of a 13th-century carol during his holiday visit to Aachen cathedral.
And Schipke says "I was stunned. It was like finding a picture of Bill Gates in the Dead Sea Scrolls".
The article contains "References" which includes the following line:
[5] Schipke, R.J. and Eberhardt, A. "The forgotten genius of Udo von Aachen", Harvard Journal of Historical Mathematics, 32, 3 (March 1999), pp 34-77.
And the article is closed with the following :
© Ray Girvan (ray@raygirvan.co.uk), April 1st 1999.
My sincere thanks to the late Bob Schipke for permission to reproduce his work.
It is such a highly elaborate hoax. It has a Wiki page "Udo of Aachen".
I wish his text won't be falsified to replace Bill Gates' name to vermin like f*Elon 仮面 or 雑貨虫 🪳
There was another hoax referring to FLT using Mason–Stothers theorem, a corollary of which is the analog of Fermat's Last Theorem for function fields.
However, If you find something like
"π (Pi) does not exist" or
"transcendental numbers do not exist",
they are not April Fools' Day hoaxes, but the authors talk what they don't understand.
Back to "Prime Days", there're 22 "Prime Days" in 2025 as follows:
20250101, 20250121, 20250203, 20250227, 20250317,
20250401 (⬅️Today), 20250413, 20250421, 20250509,
20250701, 20250707, 20250809, 20250821, 20250907,
20251013, 20251027, 20251103, 20251123, 20251129,
20251211, 20251223, 20251229
In 21st century, the 1st of April becomes a "Prime Day" in the following years:
2009, 2010, 2016, 2021,
2025 (⬅️This year), 2028, 2031,
2034, 2057, 2064, 2070,
2076, 2090, 2091, 2093
These are not considered mathematics, though…
One can generate lots of easy quizzes such as:
❓Are there any YYYYMMDD format 8 digit numbers of a square (i.e. YYYYMMDD = n² for some n ∊ N) with YYYY between 2001 and 2100 ?
➡️This is a straightforward calculation…
20151121 = 4489² = 67⁴
20241001 = 4499² = 11² × 409²
20720704 = 4552² = 2⁶ × 569²
20930625 = 4575² = 3² × 5⁴ × 61²
❓When 29th of February becomes a "Prime Day" in 21st century ?
➡️A simple calculation results in the following numbers:
20070229, 20110229, 20250229, 20280229,
20490229, 20500229, 20520229, 20530229,
20580229, 20650229, 20770229, 20800229,
20950229, 21000229
According to the definition of a leap year 閏年, the answer is
20520229 & 20800229
😎
"Plank, plonk, plink" in the title of this article, is not "Plink, Plank, Plunk" by Leroy Anderson, but is found in the following book I read long time ago:
■